Multiparticle collision dynamics simulations of hydrodynamic interactions in colloidal suspensions: How well does the discrete particle approach do at short range?

The multiparticle collision dynamics (MPCD) simulation method is an attractive technique for studying the effects of hydrodynamic interactions in colloidal suspensions because of its flexibility, computational efficiency, and ease of implementation. Here, we analyze an extension of the basic MPCD method in which colloidal particles are discretized with a surface mesh of sensor nodes/particles that interact with solvent particles (MPCD + Discrete Particle or MPCD + DP). We use several situations that have been described analytically to probe the impact of colloidal particle mesh resolution on the ability of the MPCD + DP method to resolve short-ranged hydrodynamic interactions, which are important in crowded suspensions and especially in self-assembling systems that create high volume fraction phases. Specifically, we consider (A) hard-sphere diffusion near a wall, (B) two-particle diffusion, (C) hard-sphere diffusion in crowded suspensions, and (D) the dynamics of aggregation in an attractive colloidal suspension. We show that in each case, the density of sensor nodes plays a significant role in the accuracy of the simulation and that a surprisingly high number of surface nodes are needed to fully capture hydrodynamic interactions.

A unified theory of free energy functionals and applications to diffusion.

SignificanceThe free energy functional is a central component of continuum dynamical models used to describe phase transitions, microstructural evolution, and pattern formation. However, despite the success of these models in many areas of physics, chemistry, and biology, the standard free energy frameworks are frequently characterized by physically opaque parameters and incorporate assumptions that are difficult to assess. Here, we introduce a mathematical formalism that provides a unifying umbrella for constructing free energy functionals. We show that Ginzburg-Landau framework is a special case of this umbrella and derive a generalization of the widely employed Cahn-Hilliard equation. More broadly, we expect the framework will also be useful for generalizing higher-order theories, establishing formal connections to microscopic physics, and coarse graining.

Predicting risk for trauma patients using static and dynamic information from the MIMIC III database.

Risk quantification algorithms in the ICU can provide (1) an early alert to the clinician that a patient is at extreme risk and (2) help manage limited resources efficiently or remotely. With electronic health records, large data sets allow the training of predictive models to quantify patient risk. A gradient boosting classifier was trained to predict high-risk and low-risk trauma patients, where patients were labeled high-risk if they expired within the next 10 hours or within the last 10% of their ICU stay duration. The MIMIC-III database was filtered to extract 5,400 trauma patient records (526 non-survivors) each of which contained 5 static variables (age, gender, etc.) and 28 dynamic variables (e.g., vital signs and metabolic panel). Training data was also extracted from the dynamic variables using a 3-hour moving time window whereby each window was treated as a unique patient-time fragment. We extracted the mean, standard deviation, and skew from each of these 3-hour fragments and included them as inputs for training. Additionally, a survival metric upon admission was calculated for each patient using a previously developed National Trauma Data Bank (NTDB)-trained gradient booster model. The final model was able to distinguish between high-risk and low-risk patients to an AUROC of 92.9%, defined as the area under the receiver operator characteristic curve. Importantly, the dynamic survival probability plots for patients who die appear considerably different from those who survive, an example of reducing the high dimensionality of the patient record to a single trauma trajectory.

A three-dimensional multiscale model for the prediction of thrombus growth under flow with single-platelet resolution.

Modeling thrombus growth in pathological flows allows evaluation of risk under patient-specific pharmacological, hematological, and hemodynamical conditions. We have developed a 3D multiscale framework for the prediction of thrombus growth under flow on a spatially resolved surface presenting collagen and tissue factor (TF). The multiscale framework is composed of four coupled modules: a Neural Network (NN) that accounts for platelet signaling, a Lattice Kinetic Monte Carlo (LKMC) simulation for tracking platelet positions, a Finite Volume Method (FVM) simulator for solving convection-diffusion-reaction equations describing agonist release and transport, and a Lattice Boltzmann (LB) flow solver for computing the blood flow field over the growing thrombus. A reduced model of the coagulation cascade was embedded into the framework to account for TF-driven thrombin production. The 3D model was first tested against in vitro microfluidics experiments of whole blood perfusion with various antiplatelet agents targeting COX-1, P2Y1, or the IP receptor. The model was able to accurately capture the evolution and morphology of the growing thrombus. Certain problems of 2D models for thrombus growth (artifactual dendritic growth) were naturally avoided with realistic trajectories of platelets in 3D flow. The generalizability of the 3D multiscale solver enabled simulations of important clinical situations, such as cylindrical blood vessels and acute flow narrowing (stenosis). Enhanced platelet-platelet bonding at pathologically high shear rates (e.g., von Willebrand factor unfolding) was required for accurately describing thrombus growth in stenotic flows. Overall, the approach allows consideration of patient-specific platelet signaling and vascular geometry for the prediction of thrombotic episodes.

Thrombin spatial distribution determines protein C activation during hemostasis and thrombosis.

Rebalancing the hemostatic system by targeting endogenous anticoagulant pathways, like the protein C (PC) system, is being tested as a means of improving hemostasis in patients with hemophilia. Recent intravital studies of hemostasis demonstrated that, in some vascular contexts, thrombin activity is sequestered in the extravascular compartment. These findings raise important questions about the context-dependent contribution of activated PC (APC) to the hemostatic response, because PC activation occurs on the surface of endothelial cells. We used a combination of pharmacologic, genetic, imaging, and computational approaches to examine the relationships among thrombin spatial distribution, PC activation, and APC anticoagulant function. We found that inhibition of APC activity, in mice either harboring the factor V Leiden mutation or infused with an APC-blocking antibody, significantly enhanced fibrin formation and platelet activation in a microvascular injury model, consistent with the role of APC as an anticoagulant. In contrast, inhibition of APC activity had no effect on hemostasis after penetrating injury of the mouse jugular vein. Computational studies showed that differences in blood velocity, injury size, and vessel geometry determine the localization of thrombin generation and, consequently, the extent of PC activation. Computational predictions were tested in vivo and showed that when thrombin generation occurred intravascularly, without penetration of the vessel wall, inhibition of APC significantly increased fibrin formation in the jugular vein. Together, these studies show the importance of thrombin spatial distribution in determining PC activation during hemostasis and thrombosis.

A 1D-3D Hybrid Model of Patient-Specific Coronary Hemodynamics.

PURPOSE: Coronary flow is affected by evolving events such as atherosclerotic plaque formation, rupture, and thrombosis, resulting in myocardial ischemia and infarction. Highly resolved 3D hemodynamic data at the stenosis is essential to model shear-sensitive thrombotic events in coronary artery disease. METHODS: We developed a hybrid 1D-3D simulation framework to compute patient-specific coronary hemodynamics efficiently. A 1D model of the coronary flow is coupled to an image-based 3D model of the region of interest. This framework affords the advantages of reduced-order modeling, decreasing the global computational cost, without sacrificing the accuracy of the quantities of interest. RESULTS: We validated our 1D-3D model against full 3D coronary simulations in healthy and diseased conditions. Our results showed good agreement between the 3D and the 1D-3D models while reducing the computational cost by 40-fold compared to the 3D simulation. The 1D-3D model predicted left/right coronary flow distribution within 3% and provided an accurate estimation of fractional flow reserve and wall shear stress distribution at the stenosis comparable to the 3D simulation. CONCLUSION: Savings in computational cost may be significant in situations with changing geometry, such as growing thrombosis. Also, this approach would allow quantifying the time-dependent effect of thrombotic growth and occlusion on the global coronary circulation.

Thrombosis and Hemodynamics: external and intrathrombus gradients.

Distinct from dilute, isotropic, and homogeneous reaction systems typically used in laboratory kinetic assays, blood is concentrated, two-phase, flowing, and highly anisotropic when clotting on a surface. This review focuses on spatial gradients that are generated and can dictate thrombus structure and function. Novel experimental and computational tools have recently emerged to explore reaction-transport coupling during clotting. Multiscale simulations help bridge tissue length scales (the coronary arteries) to millimeter scales of a growing clot to the microscopic scale of single-cell signaling and adhesion. Microfluidic devices help create and control pathological velocity profiles, albeit at a low Reynolds number. Since rate processes and force loading are often coupled, this review highlights prevailing convective-diffusive transport physics that modulate cellular and molecular processes during thrombus formation.

Shear-driven rolling of DNA-adhesive microspheres.

Many biologically important cell binding processes, such as the rolling of leukocytes in the vasculature, are multivalent, being mediated by large numbers of weak binding ligands. Quantitative agreement between experiments and models of rolling has been elusive and often limited by the poor understanding of the binding and unbinding kinetics of the ligands involved. Here, we present a cell-free experimental model for such rolling, consisting of polymer microspheres whose adhesion to a glass surface is mediated by ligands with well-understood force-dependent binding free energy-short complementary DNA strands. We observe robust rolling activity for certain values of the shear rate and the grafted DNA strands' binding free energy and force sensitivity. The simulation framework developed to model leukocyte rolling, adhesive dynamics, quantitatively captures the mean rolling velocity and lateral diffusivity of the experimental particles using known values of the experimental parameters. Moreover, our model captures the velocity variations seen within the trajectories of single particles. Particle-to-particle variations can be attributed to small, plausible differences in particle characteristics. Overall, our findings confirm that state-of-the-art adhesive dynamics simulations are able to capture the complex physics of particle rolling, boding well for their extension to modeling more complex systems of rolling cells.

Using the National Trauma Data Bank (NTDB) and machine learning to predict trauma patient mortality at admission.

A 400-estimator gradient boosting classifier was trained to predict survival probabilities of trauma patients. The National Trauma Data Bank (NTDB) provided 799233 complete patient records (778303 survivors and 20930 deaths) each containing 32 features, a number further reduced to only 8 features via the permutation importance method. Importantly, the 8 features can all be readily determined at admission: systolic blood pressure, heart rate, respiratory rate, temperature, oxygen saturation, gender, age and Glasgow coma score. Since death was rare, a rebalanced training set was used to train the model. The model is able to predict a survival probability for any trauma patient and accurately distinguish between a deceased and survived patient in 92.4% of all cases. Partial dependence curves (Psurvival vs. feature value) obtained from the trained model revealed the global importance of Glasgow coma score, age, and systolic blood pressure while pulse rate, respiratory rate, temperature, oxygen saturation, and gender had more subtle single variable influences. Shapley values, which measure the relative contribution of each of the 8 features to individual patient risk, were computed for several patients and were able to quantify patient-specific warning signs. Using the NTDB to sample across numerous patient traumas and hospital protocols, the trained model and Shapley values rapidly provides quantitative insight into which combination of variables in an 8-dimensional space contributed most to each trauma patient's predicted global risk of death upon emergency room admission.

Hydrodynamic and frictional modulation of deformations in switchable colloidal crystallites.

Displacive transformations in colloidal crystals may offer a pathway for increasing the diversity of accessible configurations without the need to engineer particle shape or interaction complexity. To date, binary crystals composed of spherically symmetric particles at specific size ratios have been formed that exhibit floppiness and facile routes for transformation into more rigid structures that are otherwise not accessible by direct nucleation and growth. There is evidence that such transformations, at least at the micrometer scale, are kinetically influenced by concomitant solvent motion that effectively induces hydrodynamic correlations between particles. Here, we study quantitatively the impact of such interactions on the transformation of binary bcc-CsCl analog crystals into close-packed configurations. We first employ principal-component analysis to stratify the explorations of a bcc-CsCl crystallite into orthogonal directions according to displacement. We then compute diffusion coefficients along the different directions using several dynamical models and find that hydrodynamic correlations, depending on their range, can either enhance or dampen collective particle motions. These two distinct effects work synergistically to bias crystallite deformations toward a subset of the available outcomes.

Coagulopathy implications using a multiscale model of traumatic bleeding matching macro- and microcirculation.

Quantifying the relationship between vascular injury and the dynamic bleeding rate requires a multiscale model that accounts for changing and coupled hemodynamics between the global and microvascular levels. A lumped, global hemodynamic model of the human cardiovascular system with baroreflex control was coupled to a local 24-level bifurcating vascular network that spanned diameters from the muscular artery scale (0.1-1.3 mm) to capillaries (5-10 µm) via conservation of momentum and conservation of mass boundary conditions. For defined injuries of severing all vessels at each nth-level, the changing pressures and flowrates were calculated using prescribed shear-dependent hemostatic clot growth rates (normal or coagulopathic). Key results were as follows: 1) the upstream vascular network rapidly depressurizes to reduce blood loss; 2) wall shear rates at the hemorrhaging wound exit are sufficiently high (~10,000 s-1) to drive von Willebrand factor unfolding; 3) full coagulopathy results in >2-liter blood loss in 2 h for severing all vessels of 0.13- to 0.005-mm diameter within the bifurcating network, whereas full hemostasis limits blood loss to <100 ml within 2 min; and 4) hemodilution from transcapillary refill increases blood loss and could be implicated in trauma-induced coagulopathy. A sensitivity analysis on length-to-diameter ratio and branching exponent demonstrated that bleeding was strongly dependent on these tissue-dependent network parameters. This is the first bleeding model that prescribes the geometry of the injury to calculate the rate of pressure-driven blood loss and local wall shear rate in the presence or absence of coagulopathic blood. NEW & NOTEWORTHY We developed a multiscale model that couples a lumped, global hemodynamic model of a patient to resolved, single-vessel wounds ranging from the small artery to capillary scale. The model is able to quantify wall shear rates, seal rates, and blood loss rates in the presence and absence of baroreflex control and hemodilution.

Carbon solubility in liquid silicon: A computational analysis across empirical potentials.

The nucleation and growth of SiC precipitates in liquid silicon is important in the crystallization of silicon used for the photovoltaic industry. These processes depend strongly on the carbon concentration as well as the equilibrium solubility relative to the precipitate phase. Here, using a suite of statistical thermodynamic techniques, we calculate the solubility of carbon atoms in liquid silicon relative to the ß-SiC phase. We employ several available empirical potentials to assess whether these potentials may reasonably be used to computationally analyze SiC precipitation. We find that some of the Tersoff-type potentials provide an excellent picture for carbon solubility in liquid silicon but, because of their severe silicon melting point overestimation, are limited to high temperatures where the carbon solubility is several percent, a value that is irrelevant for typical solidification conditions. Based on chemical potential calculations for pure silicon, we suggest that this well-known issue is confined to the description of the liquid phase and demonstrate that some recent potential models for silicon might address this weakness while preserving the excellent description of the carbon-silicon interaction found in the existing models.

A parallel fluid-solid coupling model using LAMMPS and Palabos based on the immersed boundary method.

The study of viscous fluid flow coupled with rigid or deformable solids has many applications in biological and engineering problems, e.g., blood cell transport, drug delivery, and particulate flow. We developed a partitioned approach to solve this coupled Multiphysics problem. The fluid motion was solved by Palabos (Parallel Lattice Boltzmann Solver), while the solid displacement and deformation was simulated by LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator). The coupling was achieved through the immersed boundary method (IBM). The code modeled both rigid and deformable solids exposed to flow. The code was validated with the Jeffery orbits of an ellipsoid particle in shear flow, red blood cell stretching test, and effective blood viscosity flowing in tubes. It demonstrated essentially linear scaling from 512 to 8192 cores for both strong and weak scaling cases. The computing time for the coupling increased with the solid fraction. An example of the fluid-solid coupling was given for flexible filaments (drug carriers) transport in a flowing blood cell suspensions, highlighting the advantages and capabilities of the developed code.

Deposition of sticky spheres in channel flow: Modeling of surface coverage evolution requires accurate sphere-sphere collision hydrodynamics.

We analyzed the role of hydrodynamic interactions in a microfluidic channel flow containing a dilute suspension of micron-scale colloidal spheres (0.03%, 0.1%, 0.3% volume fraction) engineered to adhere onto a collector patch on the channel wall at wall shear rates of 9.3-930 s-1. Particle-wall adhesion was mediated by single-stranded DNA oligomers grafted onto the spheres and the glass channel wall, producing well-defined interactions via DNA strand base pairing. Particle positions in the flow were evolved using Brownian dynamics simulations in which hydrodynamic interactions between moving particles and the channel walls and/or adhered particles were computed off-line using a series of local simulations that explicitly resolve the fluid flow at the particle scale. By systematically varying the nature of hydrodynamic interactions captured in the Brownian dynamics simulations, we find that the interactions between moving and adhered particles represents the single most important physical element in such models. Once captured sufficiently accurately, the resulting models are able to predict coarse variables such as the overall particle coverage evolution, as well as more subtle characteristics, such as the microstructural distribution of the adhered particles.

Multiscale systems biology of trauma-induced coagulopathy.

Trauma with hypovolemic shock is an extreme pathological state that challenges the body to maintain blood pressure and oxygenation in the face of hemorrhagic blood loss. In conjunction with surgical actions and transfusion therapy, survival requires the patient's blood to maintain hemostasis to stop bleeding. The physics of the problem are multiscale: (a) the systemic circulation sets the global blood pressure in response to blood loss and resuscitation therapy, (b) local tissue perfusion is altered by localized vasoregulatory mechanisms and bleeding, and (c) altered blood and vessel biology resulting from the trauma as well as local hemodynamics control the assembly of clotting components at the site of injury. Building upon ongoing modeling efforts to simulate arterial or venous thrombosis in a diseased vasculature, computer simulation of trauma-induced coagulopathy is an emerging approach to understand patient risk and predict response. Despite uncertainties in quantifying the patient's dynamic injury burden, multiscale systems biology may help link blood biochemistry at the molecular level to multiorgan responses in the bleeding patient. As an important goal of systems modeling, establishing early metrics of a patient's high-dimensional trajectory may help guide transfusion therapy or warn of subsequent later stage bleeding or thrombotic risks. This article is categorized under: Analytical and Computational Methods > Computational Methods Biological Mechanisms > Regulatory Biology Models of Systems Properties and Processes > Mechanistic Models.

Interaction Heterogeneity can Favorably Impact Colloidal Crystal Nucleation.

Colloidal particles with short-ranged attractions, e.g., micron-scale spheres functionalized with single-stranded DNA oligomers, are susceptible to becoming trapped in disordered configurations even when a crystalline arrangement is the ground state. Moreover, for reasons that are not well understood, seemingly minor variations in the particle formulation can lead to dramatic changes in the crystallization outcome. We demonstrate, using a combination of equilibrium and nonequilibrium computer simulations, that interaction heterogeneity-variations in the energetic interactions among different particle pairs in the population-may favorably impact crystal nucleation. Specifically, interaction heterogeneity is found to lower the free energy barrier to nucleation via the formation of clusters comprised preferentially of strong-binding particle pairs. Moreover, gelation is inhibited by "spreading out over time" the nucleation process, resulting in a reduced density of stable nuclei, allowing each to grow unhindered and larger. Our results suggest a simple and robust approach for enhancing colloidal crystallization near the "sticky sphere" limit, and support the notion that differing extents of interaction heterogeneity arising from various particle functionalization protocols may contribute to the otherwise unexplained variations in crystallization outcomes reported in the literature.

Self-assembly with colloidal clusters: facile crystal design using connectivity landscape analysis.

Recent experimental and theoretical studies demonstrate that prefabricated micron-scale colloidal clusters functionalized with DNA oligomers offer a practical way for introducing anisotropic interactions, significantly extending the scope of DNA-mediated colloidal assembly, and enabling the formation of interesting crystalline superstructures that are otherwise inaccessible with short-ranged, spherically symmetric interactions. However, it is apparent that the high-dimensional parameter space that defines the geometric and interaction properties of such systems poses an obstacle to assembly design and optimization. Here, we present a geometrical analysis that generates connectivity landscapes for target superstructures, greatly reducing the space over which subsequent experimental trials must search. We focus on several superstructures that are assembled from binary systems comprised of 'merged' or 'sintered' tetrahedral clusters and single spheres. We also validate and extend the analytical constraint approach with direct MD simulations of superstructure nucleation and growth.

Colloidal crystals with diamond symmetry at optical lengthscales.

Future optical materials promise to do for photonics what semiconductors did for electronics, but the challenge has long been in creating the structure they require-a regular, three-dimensional array of transparent microspheres arranged like the atoms in a diamond crystal. Here we demonstrate a simple approach for spontaneously growing double-diamond (or B32) crystals that contain a suitable diamond structure, using DNA to direct the self-assembly process. While diamond symmetry crystals have been grown from much smaller nanoparticles, none of those previous methods suffice for the larger particles needed for photonic applications, whose size must be comparable to the wavelength of visible light. Intriguingly, the crystals we observe do not readily form in previously validated simulations; nor have they been predicted theoretically. This finding suggests that other unexpected microstructures may be accessible using this approach and bodes well for future efforts to inexpensively mass-produce metamaterials for an array of photonic applications.

Multiscale simulation of thrombus growth and vessel occlusion triggered by collagen/tissue factor using a data-driven model of combinatorial platelet signalling.

During clotting under flow, platelets bind and activate on collagen and release autocrinic factors such as ADP and thromboxane, while tissue factor (TF) on the damaged wall leads to localized thrombin generation. Towards patient-specific simulation of thrombosis, a multiscale approach was developed to account for: platelet signalling [neural network (NN) trained by pairwise agonist scanning (PAS), PAS-NN], platelet positions (lattice kinetic Monte Carlo, LKMC), wall-generated thrombin and platelet-released ADP/thromboxane convection-diffusion (partial differential equation, PDE) and flow over a growing clot (lattice Boltzmann). LKMC included shear-driven platelet aggregate restructuring. The PDEs for thrombin, ADP and thromboxane were solved by finite element method using cell activation-driven adaptive triangular meshing. At all times, intracellular calcium was known for each platelet by PAS-NN in response to its unique exposure to local collagen, ADP, thromboxane and thrombin. When compared with microfluidic experiments of human blood clotting on collagen/TF driven by constant pressure drop, the model accurately predicted clot morphology and growth with time. In experiments and simulations at TF at 0.1 and 10 molecule-TF/$\mu$m$^{2}$ and initial wall shear rate of 200 s$^{-1}$, the occlusive blockade of flow for a 60-$\mu$m channel occurred relatively abruptly at 600 and 400 s, respectively (with no occlusion at zero TF). Prior to occlusion, intrathrombus concentrations reached 50 nM thrombin, ~ 1 $\mu$M thromboxane and ~ 10 $\mu$M ADP, while the wall shear rate on the rough clot peaked at ~ 1000-2000 s$^{-1}$. Additionally, clotting on TF/collagen was accurately simulated for modulators of platelet cyclooxygenase-1, P2Y$_{1}$ and IP-receptor. This multiscale approach facilitates patient-specific simulation of thrombosis under hemodynamic and pharmacological conditions.

Analysis of the lattice kinetic Monte Carlo method in systems with external fields.

The lattice kinetic Monte Carlo (LKMC) method is studied in the context of Brownian particles subjected to drift forces, here principally represented by external fluid flow. LKMC rate expressions for particle hopping are derived that satisfy detailed balance at equilibrium while also providing correct dynamical trajectories in advective-diffusive situations. Error analyses are performed for systems in which collections of particles undergo Brownian motion while also being advected by plug and parabolic flows. We demonstrate how the flow intensity, and its associated drift force, as well as its gradient, each impact the accuracy of the method in relation to reference analytical solutions and Brownian dynamics simulations. Finally, we show how a non-uniform grid that everywhere retains full microscopic detail may be employed to increase the computational efficiency of lattice kinetic Monte Carlo simulations of particles subjected to drift forces arising from the presence of external fields.